Circle Corner

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • circle corner 1circle corner 5Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
  • Chord is a line segment on the interior of a circle.
  • Segment of a circle is an interior part of a circle bound by a chord and an arc.

 

area of a Circle Corner formula

\(\large{ A = \frac{a\;b \;-\; r \; L \;+\; c \; \left(r \;-\; h\right)  }{2 }   }\)   

Where:

Units  English Metric
\(\large{ A }\) = area \(\large{ft^2}\) \(\large{m^2}\)
\(\large{ L }\) = arc length \(\large{ft}\) \(\large{m}\)
\(\large{ c }\) = chord length \(\large{ft}\) \(\large{m}\)
\(\large{ a, b }\) = edge \(\large{ft}\) \(\large{m}\)
\(\large{ r }\) = radius \(\large{ft}\) \(\large{m}\)
\(\large{ h }\) = segment height \(\large{ft}\) \(\large{m}\)

 

Arc Length of a Circle Corner formula

\(\large{ L =  r \; \Delta }\)   

Where:

Units  English Metric
\(\large{ L }\) = arc length \(\large{ft}\) \(\large{m}\)
\(\large{ \Delta }\) = angle \(\large{deg}\) \(\large{rad}\)
\(\large{ r }\) = radius \(\large{ft}\) \(\large{m}\)

 

Chord Length of a Circle Corner formula

\(\large{ c = a^2 \; b^2   }\)   

Where:

Units English Metric
\(\large{ c }\) = chord length \(\large{ft}\) \(\large{m}\)
\(\large{ a, b }\) = edge \(\large{ft}\) \(\large{m}\)

 

Height of a Circle Corner formula

\(\large{ h = r \; \left( 1 - cos \; \frac{\Delta}{2} \right)    }\)   

Where:

Units English Metric
\(\large{ h }\) = segment height \(\large{ft}\) \(\large{m}\)
\(\large{ \Delta }\) = segment angle \(\large{deg}\) \(\large{rad}\)
\(\large{ r }\) = radius \(\large{ft}\) \(\large{m}\) 

 

Perimeter of a Circle Corner formula

\(\large{ p = a + b + L   }\)   

Where:

Units English Metric
\(\large{ p }\) = perimeter \(\large{ft}\) \(\large{m}\)
\(\large{ L }\) = arc length \(\large{ft}\) \(\large{m}\)
\(\large{ a, b }\) = edge \(\large{ft}\) \(\large{m}\) 

 

Segment Angle of a Circle Corner formula

\(\large{ \Delta =   arccos \;  \frac{ 2\;r^2 \;-\; c^2 }{2\;r^2}  }\)   

Where:

Units English Metric
\(\large{ \Delta }\) = segment angle \(\large{deg}\) \(\large{rad}\)
\(\large{ c }\) = chord length \(\large{ft}\) \(\large{m}\)
\(\large{ r }\) = radius \(\large{ft}\) \(\large{m}\)  

 

Piping Designer Logo 1 

Tags: Area Equations Perimeter Equations Arc Length Equations Chord Equations Segment Equations